On the Study of Nonlinear Capillarity Models Through Weighted Sobolev Spaces with Dirichlet Boundary Conditions

Q: What type of study is this?

This is a Quantitative Study study.

Manal Badgaish; Lhoucine Hmidouch; Nacir Hmidouch

doi:10.3390/math13203353

October 21, 2025MathematicsOpen Access

On the Study of Nonlinear Capillarity Models Through Weighted Sobolev Spaces with Dirichlet Boundary Conditions

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Key Points

Weak solutions exist for nonlinear degenerate parabolic problems involving capillarity phenomena, and are proven through rigorous analysis.
The core finding confirms the unique nature of solutions under Dirichlet boundary conditions for specific mathematical models.
Analysis performed on weighted Sobolev spaces enhances understanding of the behavior of capillarity models under specified conditions.
The implications may influence further research in mathematical modeling of capillarity in physical systems, highlighting foundational concepts.

Implication

Analysis reveals unique weak solutions for nonlinear degenerate parabolic problems, indicating capillarity dynamics are possible.

Abstract

We prove in this paper some existence and uniqueness results of weak solutions for some nonlinear degenerate parabolic problems arising from capillarity phenomena with the Dirichlet type boundary condition.

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Cite This Study

Badgaish et al. (2025) studied this question.

synapsesocial.com/papers/68f9f86eb2c35e10cc4e3be4 https://doi.org/10.3390/math13203353

View Full Paper

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On the Study of Nonlinear Capillarity Models Through Weighted Sobolev Spaces with Dirichlet Boundary Conditions

Key Points

Implication

Abstract

Discussion

Cite This Study

On the Study of Nonlinear Capillarity Models Through Weighted Sobolev Spaces with Dirichlet Boundary Conditions

Key Points

Implication

Abstract

Discussion

Cite This Study

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